In this paper we investigate panel regression models with interactive fixed effects. We propose two new estimation methods that are based on minimizing convex objective functions. The first method minimizes the sum of squared residuals with a nuclear (trace) norm regularization. The second method minimizes the nuclear norm of the residuals. We establish the consistency of the two resulting estimators. Those estimators have a very important computational advantage compared to the existing least squares (LS) estimator, in that they are defined as minimizers of a convex objective function. In addition, the nuclear norm penalization helps to resolve a potential identification problem for interactive fixed effect models, in particular when the regressors are low-rank and the number of the factors is unknown. We also show how to construct estimators that are asymptotically equivalent to the least squares (LS) estimator in Bai (2009) and Moon and Weidner (2017) by using our nuclear norm regularized or minimized estimators as initial values for a finite number of LS minimizing iteration steps. This iteration avoids any non-convex minimization, while the original LS estimation problem is generally non-convex, and can have multiple local minima.

翻译：本文研究具有交互固定效应的面板回归模型。我们提出了两种基于凸目标函数最小化的新估计方法。第一种方法在核（迹）范数正则化下最小化残差平方和。第二种方法最小化残差的核范数。我们证明了两种估计量的一致性。与现有的最小二乘（LS）估计量相比，这些估计量具有非常重要的计算优势，因为它们被定义为凸目标函数的最小化器。此外，核范数惩罚有助于解决交互固定效应模型潜在的识别问题，特别是当回归变量为低秩且因子数量未知时。我们还展示了如何通过将我们的核范数正则化或最小化估计量作为有限次LS最小化迭代步骤的初始值，来构建与Bai（2009）及Moon和Weidner（2017）中最小二乘（LS）估计量渐近等价的估计量。该迭代避免了任何非凸最小化问题，而原始的LS估计问题通常是非凸的，并且可能具有多个局部极小值。